Thermomagnetic Convection Research Articles

A numerical study on heat transfer of a ferrofluid flow in a square cavity under simultaneous gravitational and magnetic convection

Thermomagnetic convection is based on the use of external magnetic fields to better control heat transfer fluxes in ferrofluids, finding important applications in engineering and many related areas. The improvement of such methods relies on fundamentally understanding the flow of ferrofluids under temperature gradients and external magnetic fields. However, the underlying physics of this phenomenon is very complex and not yet well characterized. The problem we analyze in this paper consists of a ferrofluid confined in a square cavity heated from the top and subjected to an external magnetic field applied in the horizontal direction. Differently from earlier investigations, this scenario leads to a clear competition between stabilizing gravitational forces and destabilizing magnetic forces; the unbalance between them drives the flow and dictates the mechanisms of heat transfer in the system. The problem is described by the equations of conservation of mass, momentum, and energy; both gravitational and magnetic effects are accounted for through the definition of the body force following the well-known Boussinesq approximation to express the ferrofluid’s density and magnetization as functions of temperature. The resulting set of fully coupled, nonlinear equations of the model is solved with a fully implicit finite element method. The results show that thermomagnetic convection increases convective heat transfer fluxes in the flow, but its net effects essentially depend on a complex balance among viscous, magnetic, and gravitational forces which determines the pattern of recirculation regions inside the cavity. There are two critical values associated with the external field’s intensity: the first marks the onset of thermomagnetic convection when the destabilizing magnetic effects become comparable to the stabilizing gravitational ones and the second corresponds to the external field’s strength that suffices to make the effects of gravity nearly negligible in the flow dynamics. The latter regime is dictated by a balance between viscous and magnetic forces only, and the corresponding numerical predictions agree notoriously well with a scaling analysis which suggests that $${\overline{\mathrm{Nu}}} \sim \mathrm{Ra}_\mathrm{m}^{1/4}$$, where $${\overline{\mathrm{Nu}}}$$ is the average Nusselt number at the isothermal walls and $$\mathrm{Ra}_\mathrm{m}$$ is the magnetic Rayleigh number, a dimensionless parameter associated with the intensity of the external field.

A monotone finite-difference high order accuracy scheme for the 2D convection – diffusion equations

A stable finite-difference scheme is constructed on a minimum stencil of a uniform mesh for a two-dimensional steady-state convection – diffusion equation of a general form; the scheme is theoretically studied and tested. It satisfies the maximum principle and has the fourth order of approximation. The scheme monotonicity is controlled by two regularization parameters introduced into the difference operator. The scheme is focused on solving applied convection – diffusion problems with a developed boundary layer, including gravitational convection, thermomagnetic convection, and diffusion of particles in a magnetic fluid. The scheme is tested on the well-known problem of a high-intensive gravitational convection in a horizontal channel of a square cross-section with a uniform heating from the side. A detailed comparison is performed with the monotone Samarskii scheme of the second order approximation on the sequences of square meshes with the number of partitions from 10 to 1000 on each side of the square domain and over the entire range of the Rayleigh numbers, corresponding to the laminar convection mode. A significant advantage of the fourth order scheme in the convergence rate is shown for the decreasing mesh step.

Numerical simulations and linear stability analysis of mixed thermomagnetic convection through two lid-driven entrapped trapezoidal cavities enclosing ferrofluid saturated porous medium

This paper presents computational results for mixed convective heat flow through porous medium within two entrapped trapezoidal cavities filled of kerosene‑cobalt ferrofluid placed under the influence of magnetic field when heat is provided through uniformly moving top and bottom horizontal boundaries, however, the inclined walls are cold whereas middle horizontal wall is assumed insulated. Galerkin weighted residual scheme is employed to carry out the numerical results for analysis of considered flow problem. Obtained solutions are illustrated through graphs of streamlines, isotherms, local and average heat transfer rates. Results show that, the patterns of energy and fluid flow are significantly dependent upon the concentration of solid ferro particles, Grashof, Darcy and Hartman numbers.

Effect of uniform external magnetic-field on natural convection heat transfer in a cubical cavity filled with magnetic nano-dispersion

Heat transfer in magnetic nano-particle dispersion can be influenced by the presence of external magnetic-field. This paper presents an experimental investigation on effect of external uniform magnetic-field on natural convection heat transfer in magnetite and iron nano-dispersion in a differentially heated cubical cavity. The experiments are conducted between the Rayleigh number range of 4.23×105 to 1.0×107. The study includes experiments and discussion on the corroborating and suppressing effects of thermo-magnetic convection induced by the external magnetic-field on the natural convection heat transfer. Additionally, this study also reports the experimental results and pertinent explanation on the directional effect of magnetic-field on the heat transfer in magnetite and iron nano-dispersion. The paper quantitatively presents the extent of heat transfer depreciation/enhancement in different orientations of the cavity in the presence of magnetic-field. The study also explores the effect of particle volume fraction in magnetic fluid on heat transfer in each case.

Thermomagnetic Convection of Ferrofluid in an Enclosure Channel with an Internal Magnetic Field.

Ferrofluid is a colloidal liquid in which magnetic nanoparticles such as Fe3O4 are dispersed in a nonconductive solution, and the average diameter of the nanoparticles is 10 nm. When a magnetic field is applied, the ferrofluid generates magnetization, which changes the physical properties of the fluid itself. In this study, characteristics of the thermomagnetic convection of ferrofluid (Fe3O4) by the permanent magnet in the enclosure channel were studied. To effectively mix the ferrofluid (Fe3O4) and disturb the boundary layer, the heat dissipation of the heat source depending on the strength of the magnetic field and the shape of the enclosure channel was numerically studied. In particular, four different enclosure channels were considered: Square, separated square, circle, and separated circle. The hot temperature was set at the center of the enclosure channel. The ferrofluid was affected by the permanent magnet in the center of the channel. The magnetic field strength in the region close to the permanent magnet was enhanced. The magnetophoretic (MAP) force increased with increasing magnetic field strength. The MAP force generated a vortex in the enclosure channel, disturbing the thermal boundary. The vortex occurs differently, depending on the shape of the enclosure channel and affects the thermomagnetic convection. The temperature and velocity fields for thermomagnetic convection were described and the convective heat flux was calculated and compared. Results show that when the magnetic field strength was 4000 kA/m and the shape of the enclosure channel was a circle, the maximum convective heat flux of 4.86 × 105 W/m2 was obtained.

Transformer oil-based magnetic nanofluid with high dielectric losses tested for cooling of a model transformer

An experimental study of dielectric permittivity and dissipation factor of transformer oil-based magnetic nanofluid is reported in this paper. The investigated nanofluid consists of a commercial transformer oil and iron oxide nanoparticles (0.93 % solid volume fraction) coated with oleic acid as a stabilizing agent. Both, the transformer oil and the nanofluid were subjected to measurements of dielectric permittivity and dissipation factor under 1 kV at a power frequency of 50 Hz in the temperature range from 303 to 373 K. The compared results show that the magnetic nanofluid exhibits approximately 4 orders of magnitude greater dielectric losses than the transformer oil. This raised a question about the suitability of such a nanofluid for cooling applications in a transformer. Therefore, the cooling effectiveness of the nanofluid was tested in a model single-phase power transformer under 4.3 kVA load. The prototype transformer was designed with the aim to monitor its temperature at various locations during the load test. It was found that the cooling with the lossy nanofluid does not result in the deterioration of the thermal conditions of the transformer as compared to the cooling with the transformer oil. On the contrary, the tested nanofluid provides a slight decrease in the average transformer temperature rise. Possible reasons accounting for the slight enhancement in the transformer cooling are discussed. The increased thermal conductivity and development of thermomagnetic convection are considered as primary reasons of the cooling effect.

Entropy generation analysis for thermomagnetic convection of paramagnetic fluid inside a porous enclosure in the presence of magnetic quadrupole field

The entropy generation characteristics for thermomagnetic convection in a porous cavity filled with paramagnetic air in the presence of a magnetic quadrupole field are investigated numerically using a finite volume method. The vertical walls of the porous cavity are maintained at different temperatures, whereas the horizontal walls are insulated. The Darcy–Brinkman–Forchheimer model is used for mathematical formulation of the fluid flow in porous media. Thermal, frictional and total entropy generation and Bejan number for a selected range of magnetic force number (γ = 1–100), Darcy number (Da = 5 × 10−4–5 × 10−2) and Rayleigh number (Ra = 104–106) are examined for both cases: (1) with gravity and (2) without gravity. The results indicate that the magnetic field had little or no effect on the total entropy generation for the lower values of Darcy number and the process is dominated by the heat transfer irreversibility. In contrast, the magnetic force provokes various irreversibilities to rise as a result of improved convection at higher Darcy numbers, and the irreversibility is dominated by the viscous effects. This work may give an insight into the design-related concept of entropy generation for various thermal systems and clarifying energy loss.

A self-regulating multi-torus magneto-fluidic device for kilowatt level cooling

Efficiently removing waste heat by novel cooling devices can reduce material failure and enhance service life. Magneto-fluidic cooling, which is based on the thermomagnetic convection of a ferrofluid, offers a passive, self-regulating approach for the removal of waste heat. The performance of a novel multi-torus magnetic cooling device for kilowatt level cooling was investigated. The performance was determined for a range of heat load power. Heat load cooling increased from 148 °C to 214 °C when heat load power was increased from 0.5 kW to 1 kW, respectively, demonstrating the self-regulating nature of the device. The heat load cooling performance was assessed for various magnet positions. The temperature profile of the ferrofluid along the axial and radial directions of the flow channel revealed an asymmetric temperature distribution. The transient effect of periodic magnetic field switching on the heat load temperature was simulated using COMSOL Multiphysics and found to be in good agreement with the experimental findings. Simulated surface velocity vector plots revealed ferrofluid vortices near the heat load, these vortices resulted in enhanced mixing of hot and cold ferrofluid, leading to increased cooling. The thermal resistance of our multi-torus magnetic cooling device was determined analytically. The present device offers lower thermal resistance per unit length and lower ferrofluid thermal resistance per unit volume of ferrofluid compared to conventional heat pipes. A self pumping, self regulating passive heat pump, capable of kilowatt level cooling, has been fabricated and its cooling performance assessed.

Comparison of the experimental and numerical analyses of silver nanofluid under influence of strong magnetic field

Purpose Nanofluids’ properties made them interesting for various areas like engineering, medicine or cosmetology. Discussed here, research pertains to specific problem of heat transfer enhancement with application of the magnetic field. The main idea was to transfer high heat rates with utilization of nanofluids including metallic non-ferrous particles. The expectation was based on changed nanofluid properties. However, the results of experimental analysis did not meet it. The heat transfer effect was smaller than in the case of base fluid. The only way to understand the process was to involve the computational fluid dynamics, which could help to clarify this issue. The purpose of this research is deep understanding of the external magnetic field effect on the nanofluids heat transfer. Design/methodology/approach In presented experimental and numerical studies, the water and silver nanofluids were considered. From the numerical point of view, three approaches to model the nanofluid in the strong magnetic field were used: single-phase Euler, Euler–Euler and Euler–Lagrange. In two-phase approach, the momentum transfer equations for individual phases were coupled through the interphase momentum transfer term expressing the volume force exerted by one phase on the second one. Findings Therefore, the results of numerical simulation predicted decrease of convection heat transfer for nanofluid with respect to pure water, which agreed with the experimental results. The experimental and numerical results are in good agreement with each other, which confirms the right choice of two-phase approach in analysis of nanofluid thermo-magnetic convection. Originality/value The Euler–Lagrange exhibit the best matching with the experimental results.

Numerical simulation of combined natural and thermomagnetic convection around a current carrying wire in ferrofluid

Abstract Combined natural and thermomagnetic convection heat transfer in ferrofluid surrounding a vertically orientated electrically-heated microwire is experimentally and numerically investigated and compared with the natural convection in de-ionized water. Numerical simulation is validated with the experimental results for de-ionized water. The convective forces are induced by density and magnetic susceptibility changes both due to temperature gradients in the fluid. The results are presented in the form of a transient temperature rise of the wire and streamlines of the induced flow for different electric currents (1–2.5 A) supplied to the wire. We found that as a result of the magnetic field vortices form along the cell and enhance the heat transfer from the wire. The size and number of the vortices depend on the current supplied. The studied phenomenon can have great impact on the research on cooling electronic devices.

A segregated spectral element method for thermomagnetic convection of paramagnetic fluid in rectangular enclosures with sinusoidal temperature distribution on one side wall

An accurate segregated spectral element method is developed to simulate the thermomagnetic convection in an air-filled rectangular enclosure, which has spatially varying sinusoidal temperature distribution on the left wall with all the other walls insulated. The numerical scheme is based on spectral elements in space and the semi-implicit method for pressure linked equations algorithm is adopted to decouple the flow variables. The validation tests with analytical solution and natural convection verify the high accuracy of the algorithm. The fluid flow and heat transfer characteristics in the enclosure are systematically studied, including the influences of magnetic strength, aspect ratio, and position of the heating part. The results show that the addition of an external magnetic field significantly increases the heat transfer rate in the enclosure, and the fluid on the right side is well heated to form a uniform temperature field.

Heat storage materials based on nanomodified paraffin, controlled by a magnetic field

The article presents studies of nano-modified heat-accumulating materials controlled by a magnetic field. Paraffin is used as a material with the effect of energy accumulation in the phase transition. Carbon nanotubes are used to modify paraffin. For the synthesis of carbon nanotubes used catalyst Co-Mo/Al2O3-MgO. The synthesis process is based on the CVD method. The method of obtaining nanomodified paraffin with ferromagnetic properties is described. To impart paraffin ferromagnetic properties, a ferromagnetic powder previously ground with carbon nanotubes was introduced into it. Mechanical activation was used for the ferromagnetic powder, which provided particles with an average size of 5 ?m. The analysis of charge control regimes of a paraffin-based heat-accumulating material was carried out using a non-contact method for measuring the temperature field. For this purpose, the FLUKE Ti9 thermal imager with a 160 x 120 radiation detector and a matrix in the focal plane and a measurement range from -20 to +250? was used. The morphology and structure of the synthesized carbon nanotubes were studied by scanning electron microscopy (a Hitachi H-800 transmission electron microscope). The behavior of the modified paraffin in the conditions of mineral motor oil under the influence of electromagnetic fields was studied. The design of a heat accumulator for working with a magnetically controlled heat-accumulating material is proposed. It is established that the heat transfer in the system is provided by two simultaneously occurring processes of natural and thermomagnetic convection. In turn, convection can be realized by changing the magnetic susceptibility with a change in temperature and with a geometric change in the position of a magnet or a group of magnets.

Thermomagnetic Convection of Paramagnetic Gas in an Enclosure under No Gravity Condition

The thermomagnetic convection of paramagnetic gaseous oxygen in an enclosure under a magnetic field was numerically studied to simulate the thermomagnetic convection in a space environment with no gravity. The magnetic field in the enclosure was non-uniform and was generated by a permanent magnet which had a high magnetic energy product. The magnet was placed at different locations along one of the adiabatic walls with magnetic poles perpendicular to the hot and cold walls of the enclosure. The heat transfer performance, flow field, and temperature field were studied with each location of the magnet. The results show that the thermomagnetic convection in the enclosure was obviously affected by the location of the magnet. There was an optimum magnet location in terms of the best heat transfer performance in the enclosure. The optimum magnet location changed slightly and moved toward the hot wall as the magnetic flux density increased. The value of the Nusselt number, defined as the ratio of convection to conduction, reached up to 2.54 in the studied range of parameters. By optimizing the magnet location, the convection was enhanced by up to 77% at the optimum magnet location.

Effects of nanoparticles volume fraction and magnetic field gradient on the mixed convection of a ferrofluid in the annulus between vertical concentric cylinders

In this paper, the thermomagnetic convection of magnetite-water ferrofluid is numerically investigated in the three-dimensional space between two vertical concentric cylinders under the influence of an external magnetic field. The main objective is to study the effect of volume fraction of the magnetic nanoparticles (0.01≤αp≤0.06) with the diameter of 10 nm and positive and negative gradients of the magnetic field (-5×105A/m2≤G≤5×105A/m2) on the hydrothermal behavior of the ferrofluid flow. For this purpose, the two-phase mixture model and the finite volume method are used to simulate the hydrodynamics and thermal behavior of the ferrofluid flow. The simulations are performed for a Reynolds number of 20, Grashof number of 10000, and outer to inner diameter ratio of 2.5. The numerical results indicate that the Kelvin force increases by increasing the volume fraction, decreasing the ferrofluid temperature and increasing the magnetic field gradient. In the presence of an external magnetic field with negative gradient, the skin friction coefficient on the inner wall is enhanced by increasing the volume fraction and the magnetic field gradient but on the outer wall, it decreases by increasing them. Besides, the Nusselt number increases with the increase in the volume fraction and the magnetic field gradient. In addition, positive gradient magnetic fields result in reducing the Nusselt number and friction coefficient on the inner wall, while they increase the friction coefficient on the outer wall.

Identification of the Structures for Low Reynolds Number Flow in the Strong Magnetic Field

Thermomagnetic convection is still a phenomenon which generates interest among researchers. The authors decided to focus their attention on the magnetic field influence on forced convection and analyze the extended Graetz–Brinkman problem. A numerical model based on a commonly available solver implemented with user-defined functions was used. The results exhibited the variety of possible flow structures depending on the dimensionless parameters, namely Prandtl and Reynolds numbers. Three flow structure classes were distinguished, and they provide a platform for further research.

Effect of different frequency functions on ferrofluid FHD flow

Abstract A finite volume method is used to investigate the unsteady thermomagnetic convection of ferrofluid flow in a miniature channel under the effect of constant and oscillating magnetic fields. A magnetic line dipole as a magnetic source is placed under the lower wall of the two-dimensional channel whose lower and upper walls are subjected to a constant heat flux. To generate the oscillating magnetic field, four different frequency functions including rectangle, sine, triangle and sawtooth functions are implemented in the constant magnetic field. The study parameters include four frequency functions, magnetic field intensity as a magnetic number (Mn = 3.833 × 108, 8.624 × 108, 1.533 × 109), frequencies (f = 0.5–5 Hz) and Reynolds numbers (Re = 20–40). Results revealed that applying the constant magnetic field enhances heat transfer and as the Reynolds number increases, the effectiveness of magnetic field on heat transfer rate diminishes. The oscillating magnetic field, regardless of the type of the applied frequency function, improves heat transfer rate due to thermal boundary layer suppression and increase in velocity field. For all applied functions, results show that there is an optimum frequency where maximum heat transfer happens and this frequency increases for higher Reynolds numbers. For rectangle and sawtooth functions with instant change in the magnetic field, two simultaneous vortexes emerges which leads to better heat transfer than sine and triangle functions. The alteration of the pressure drop in one period is proportionate with the shape of the applied frequency even though the range of the alterations reduces with the increase of the Reynolds number.

Magnetoviscous effect investigation of water based Mn-Zn Fe2O4 magnetic nanofluid under the influence of magnetic field: An experimental study

Abstract This experimental study presents the magnetoviscous effect of water based Mn-Zn Fe2O4 with C-TAB as surfactant under the influence of magnetic fields. Mn-Zn Fe2O4 magnetic nanoparticles have been synthesized and characterized using correspondingly co-precipitation method and XRD, SEM and VSM analysis. Effect of various parameters like flow shear rate (0.1–1000 1/s), nanoparticle volume concentration (0.0–0.6%), sample temperature (20–60 °C) and magnetic field (0–600 A/m), has been investigated. The results show that, for the cases without magnetic field, the viscosity behaves shear thinning, Newtonian and shear thickening at respectively low, moderate, and high shear rate values. With applying magnetic fields, the larger the field strength the larger the viscosity value. Also, with nanoparticle volume fraction augmentation as well as field increase, the two shear thinning and shear thickening behaviors have been augmented; Finally, an empirical correlation is proposed to predict magnetoviscous behavior of the ferrofluid as function of the various mentioned parameters. This correlation can be helpful in thermomagnetic convection investigations.

Thermomagnetic convection in a layer of magnetic nanofluid saturating porous medium with magnetic field dependent viscosity

Thermomagnetic convection in a layer of magnetic nanofluid saturating porous medium with magnetic field dependent viscosity

Thermomagnetic convection in a layer of magnetic nanofluid saturating porous medium with magnetic field dependent viscosity

In this paper, the effect of magnetic field dependent (MFD) viscosity on the onset of thermomagnetic convection is examined for a horizontal layer of magnetic nanofluid (or ferrofluid) saturated porous layer. A model that comprises the effect of Brownian diffusion, thermophoresis, magnetophoresis, and Darcy's law is considered. We employed the Chebyshev pseudospectral QZ-method to solve the developed mathematical model and the results are derived for water-based and ester-based magnetic nanofluids. The effects of significant parameters are analysed at the onset of convection in the gravity as well as in the microgravity environment. The influence of MFD viscosity, permeability parameter, the width of the fluid layer, Lewis number, Langevin parameter, particle concentration, and the concentration Rayleigh number at the onset of thermomagnetic convection are graphically illustrated.

Direct absorption solar collector with magnetic nanofluid: CFD model and parametric analysis

Direct absorption collectors (DAC) with nanofluid are among the most promising yet least studied in solar energy technology. There are numerous micro- and macroscopic factors that determine their efficiency. This complicates in situ optimization of DACs using physical prototypes. The present paper describes a multiphase CFD model of the collector, which was validated against two independent experimental datasets. The model was used for a multiparametric numerical analysis, where we altered concentration and size of the nanoparticles, as well as the geometry and inclination of the collector. The optimization resulted in up to 10% improvement in the collector's efficiency. Finally, we considered the process of thermomagnetic convection in the collector using a magnetic nanofluid. This resulted in a 30% increase in the collector performance.